• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.293-305
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• 2023

Let {T_t}_t∈∆ be the translation semigroup with a sector ∆ ⊂ ℂ as index set. The recurrent hypercyclicity criterion (RHCC) for the C₀-semigroup {T_t}_t∈∆ is established, and then the equivalent conditions ensuring {T_t}_t∈∆ satisfying the RHCC on weighted spaces of p-integrable and of continuous functions are presented. Especially, every chaotic semigroup {T_t}_t∈∆ satisfies the RHCC.